Difficulty: Easy
Correct Answer: Rs 2522
Explanation:
Introduction:
This question applies the compound interest formula when the compounding period is quarterly. The time given is 9 months, which corresponds to three quarters of a year, so you must express the time in terms of the number of compounding periods rather than just years.
Given Data / Assumptions:
Concept / Approach:
For quarterly compounding, the annual rate is divided by 4 to get the rate per quarter, and the time in months is converted into number of quarters. The amount is given by A = P * (1 + r/(4*100))^n, where n is the number of quarters. Then CI = A − P.
Step-by-Step Solution:
Quarterly rate = 20% / 4 = 5% = 0.05 per quarterTotal time = 9 months = 9 / 3 = 3 quartersAmount after 3 quarters: A = 16000 * (1 + 0.05)^3(1.05)^2 = 1.1025 and (1.05)^3 ≈ 1.157625So A ≈ 16000 * 1.157625 = Rs 18522Compound interest CI = A − P = 18522 − 16000 = Rs 2522
Verification / Alternative Check:
Compute stepwise per quarter: after first quarter, amount = 16000 * 1.05 = 16800. After second quarter: 16800 * 1.05 = 17640. After third quarter: 17640 * 1.05 = 18522. The increase over the original principal is 18522 − 16000 = 2522, matching our previous result.
Why Other Options Are Wrong:
Rs 2422 and Rs 2322: These underestimate the compounding effect of 20% per annum when applied quarterly.Rs 3522: This overestimates the interest and might come from incorrectly using a full year instead of 9 months.Rs 2022: Much too small and likely based on a simple interest calculation.
Common Pitfalls:
Typical errors include forgetting to convert 9 months to 3 quarters or using 20% directly as the quarterly rate. Some also treat the period as 1 year, which inflates the interest. Always align the rate per period with the number of compounding periods used in the formula.
Final Answer:
The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly, is Rs 2522.
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